Conversion between Decimal Fraction and Common Fraction

• A common fraction with denominators like 10, 100, or 1000 can easily be written as a decimal fraction.

• Decimal fractions can also be converted into common fractions.

• The process helps simplify calculations and is useful in real-life scenarios, such as measuring and working with money.

When the Numerator has More Digits than Zeros in the Denominator:

Steps:

1. Count the digits from the right equal to the number of zeros in the denominator.
2. Place the decimal point before those digits.

Example:

• `51250/100` = 512.50

• Here, there are two zeros in the denominator, so place the decimal point after the second digit from the right in the numerator.

When the Numerator has Equal Digits as the Zeros in the Denominator:

Steps:

1. Place the decimal point before the number in the numerator and add a zero in the place of the integer.

Example:

• `7/10` = 0.7

• Here, the denominator is 10 (one zero), so place the decimal point after the first digit in the numerator.

When the Numerator has Fewer Digits than Zeros in the Denominator:

Steps:

1. Add zeros before the digits to match the number of zeros in the denominator.
2. Place a decimal point before them and add a zero before the decimal point.

Example:

• `8/100` = `08/100` = 0.08

• Here, the denominator is 100 (two zeros), so place the decimal point after two digits. To match the number of zeros, add a leading zero in the numerator.

1. Ignore the decimal point and write the number as it is (this becomes the numerator).

2. Count the digits after the decimal point.

• For 1 digit → write 10 as the denominator.

• For 2 digits → write 100 as the denominator.

• For 3 digits → write 1000 as the denominator, and so on.

Example:

• 19.315 = `19315/1000`
• There are three decimal places, so the denominator is 1000.

• Remember: Count zeros in denominator = decimal places to move
• For fractions: Make denominator 10, 100, or 1000 when possible
• For decimals:Number of decimal places = zeros in denominator
• Always simplify fractions to lowest terms